Test a specific exception type is thrown AND the exception has the right properties

I mostly second Lilshieste's answer but would add that you also should verify that the wrong exception type is not thrown:

#include <stdexcept>
#include "gtest/gtest.h"

struct foo
{
    int bar(int i) {
        if (i > 100) {
            throw std::out_of_range("Out of range");
        }
        return i;
    }
};

TEST(foo_test,out_of_range)
{
    foo f;
    try {
        f.bar(111);
        FAIL() << "Expected std::out_of_range";
    }
    catch(std::out_of_range const & err) {
        EXPECT_EQ(err.what(),std::string("Out of range"));
    }
    catch(...) {
        FAIL() << "Expected std::out_of_range";
    }
}

int main(int argc, char **argv) {
  ::testing::InitGoogleTest(&argc, argv);
  return RUN_ALL_TESTS();
}

A colleague came up with the solution by just re-throwing the exception.

The knack: no need of extra FAIL() statements, just the two EXPECT... calls that test the bits you actually want: the exception as such and its value.

TEST(Exception, HasCertainMessage )
{
    // this tests _that_ the expected exception is thrown
    EXPECT_THROW({
        try
        {
            thisShallThrow();
        }
        catch( const MyException& e )
        {
            // and this tests that it has the correct message
            EXPECT_STREQ( "Cucumber overflow", e.what() );
            throw;
        }
    }, MyException );
}

Jeff Langr describes a good approach in his book, Modern C++ Programming with Test-Driven Development:

If your [testing] framework does not support a single-line declarative assert that ensures an exception is thrown, you can use the following structure in your test:

    TEST(ATweet, RequiresUserNameToStartWithAnAtSign) {
        string invalidUser("notStartingWith@");
        try {
            Tweet tweet("msg", invalidUser);
            FAIL();
        }
        catch(const InvalidUserException& expected) {}
    }

[...] You might also need to use the try-catch structure if you must verify any postconditions after the exception is thrown. For example, you may want to verify the text associated with the thrown exception object.

    TEST(ATweet, RequiresUserNameToStartWithAtSign) {
        string invalidUser("notStartingWith@");
        try {
            Tweet tweet("msg", invalidUser);
            FAIL();
        }
        catch(const InvalidUserException& expected) {
            ASSERT_STREQ("notStartingWith@", expected.what());
        }
    }

(p.95)

This is the approach I've used, and have seen in practice elsewhere.

Edit: As has been pointed out by @MikeKinghan, this doesn't quite match the functionality provided by EXPECT_THROW; the test doesn't fail if the wrong exception is thrown. An additional catch clause could be added to address this:

catch(...) {
    FAIL();
}